Visualization Lab 3

# steps 4,5, 6 use euclidean distance
library(plotly)
library(seriation)

Question 1.

# keep columns 1,2,5,6,7,9,10,16,17,18,19
p_e <- prices_earnings[, c(1,2,5,6,7,9,10,16,17,18,19)]
rownames(p_e) <- p_e[[1]]

Question 2.

Without doing any reordering We cannot identify any clusters or outliers.

#p_e_sc %>% 
  plot_ly(x =~colnames(p_e_sc), y =~rownames(p_e_sc),
    z = ~p_e_sc, type = "heatmap", 
    colors = colorRamp(c("black","red"))
  ) %>%
  layout(title =  "Heatmap of prices and earnings",
         xaxis = list(title = "Price-Earnings Indicators- No order", zeroline = FALSE),
         yaxis = list(title = "Cities", zeroline = FALSE)
  )

Question 3.

# seriation needs to permute rows and columns, thus distance by row and column
p_e_rdist <- dist(p_e_sc, method = "euclidean")
p_e_cdist <- dist(t(p_e_sc), method = "euclidean")

# make sure that results are reproducible
set.seed(1011)
# get orders of the row and col distances; Hamilton path length
order1 <- get_order(seriate(p_e_rdist, method = "OLO"))
order2 <-get_order(seriate(p_e_cdist, method = "OLO"))

plot_ly(x =~colnames(p_reord), y =~rownames(p_reord),
    z = ~p_reord, type = "heatmap", 
    colors = colorRamp(c("black","red"))
  ) %>%
  layout(title =  "Heatmap of prices and earnings (Euclid dist)",
         xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
         yaxis = list(title = "Cities", zeroline = FALSE)
  )

# computing distance as one minus correlation
p_e_cor <- as.dist((1 - cor(p_e_sc))/2)
# as distance
#p_e_cor_dist <- as.dist(p_e_cor)

p_e_cor1 <- as.dist((1 - cor(t(p_e_sc)))/2)

plot_ly(x =~colnames(p_reord2), y =~rownames(p_reord2),
    z = ~p_reord2, type = "heatmap", 
    colors = colorRamp(c("black","red"))
  ) %>%
  layout(title =  "Heatmap of prices and earnings (Cor dist)",
         xaxis = list(title = "Price-Earnings Indicators", zeroline = FALSE),
         yaxis = list(title = "Cities", zeroline = FALSE)
  )

The ordering by euclidean distance produces a heat map that is easier to analyze. At first glance we can perceive four general regions of two groups. The first group heat map color tends towards a brighter shade of red while the second group tend towards a darker shade of red/black. Although these groups can be seen in the correlation distance heat map, it is not as clear as the first.

Based on the euclidean distance heat map, net wage tends to higher values from Dubai while the number of hours worked decrease. This is the opposite to cities like Delhi,Bankok and Seoul. Interestingly food costs are generally low in the cities with highee working hours. Caracas is an outlier because food costs are high while net wage and the number of hours worked remains low.

Question 4.